Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 21 to 17 computations (19% saved)

sample1.5s (52.5%)

Infinites

0% of outputs are infinite.

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 62 to 50 computations (19.4% saved)

simplify99.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
684×	`fma-neg_binary64`
640×	`associate-/l*_binary64`
583×	`associate-/r*_binary64`
496×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	34	22
2	59	22
3	94	22
4	131	22
5	171	20
6	250	20
7	423	20
8	810	20
9	1376	20
10	2197	20
11	2355	20
12	3878	20
13	4822	20
14	4656	20

prune8.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (.f64 x 4481/100000))))) x))
▶	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Status

Error

Program

0.1b

(*.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000))))) x))

▶

0.1b

(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 107 to 83 computations (22.4% saved)

localize19.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.2b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
✓	14.3b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series17.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
4.0ms	(fma.f64 x 4481/100000 99229/100000)
4.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
3.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 59

Calls

4 calls:

4.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
1.0ms	(fma.f64 x 4481/100000 99229/100000)
1.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
1.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)

simplify131.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

496×	`fma-def_binary64`
477×	`associate-l_binary64`
447×	`fma-neg_binary64`
424×	`distribute-rgt-in_binary64`
411×	`distribute-lft-in_binary64`

Counts

107 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1537
1	235	1385
2	582	1380
3	1485	1370
4	4572	1370
5	4900	1370

prune224.0ms (7.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Error

0.0b

Counts

102 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x -70711/100000 (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
	31.5b	(fma.f64 x -70711/100000 (-.f64 (+.f64 16316775383/10000000000 (.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))) (.f64 1427746267379707/1000000000000000 x)))

Compiler

Compiled 2081 to 1593 computations (23.5% saved)

localize48.0ms (1.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	0.2b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
	14.3b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

prune214.0ms (7.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	100	3	103

Error

0.0b

Counts

103 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x -70711/100000 (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
▶	31.5b	(fma.f64 x -70711/100000 (-.f64 (+.f64 16316775383/10000000000 (.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))) (.f64 1427746267379707/1000000000000000 x)))

Compiler

Compiled 2263 to 1779 computations (21.4% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x -70711/100000 (-.f64 (+.f64 16316775383/10000000000 (.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))) (.f64 1427746267379707/1000000000000000 x)))
✓	0.0b	(+.f64 16316775383/10000000000 (*.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2)))
✓	0.0b	(-.f64 (+.f64 16316775383/10000000000 (.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))) (.f64 1427746267379707/1000000000000000 x))
✓	0.2b	(*.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))

series11.0ms (0.4%)

Counts

4 → 21

Calls

4 calls:

3.0ms	(fma.f64 x -70711/100000 (-.f64 (+.f64 16316775383/10000000000 (.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))) (.f64 1427746267379707/1000000000000000 x)))
3.0ms	(*.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))
3.0ms	(+.f64 16316775383/10000000000 (*.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2)))
3.0ms	(-.f64 (+.f64 16316775383/10000000000 (.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))) (.f64 1427746267379707/1000000000000000 x))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 77

Calls

4 calls:

20.0ms	(*.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))
4.0ms	(-.f64 (+.f64 16316775383/10000000000 (.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))) (.f64 1427746267379707/1000000000000000 x))
2.0ms	(+.f64 16316775383/10000000000 (*.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2)))
0.0ms	(fma.f64 x -70711/100000 (-.f64 (+.f64 16316775383/10000000000 (.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))) (.f64 1427746267379707/1000000000000000 x)))

simplify117.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-neg_binary64`
553×	`associate-l_binary64`
518×	`associate-r_binary64`
390×	`fma-def_binary64`
218×	`exp-prod_binary64`

Counts

98 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1476
1	302	1180
2	815	1071
3	3755	1025
4	4604	1025
5	4821	1025

prune201.0ms (7.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	136	3	139

Error

0.0b

Counts

139 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x -70711/100000 (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	31.5b	(fma.f64 x -70711/100000 (-.f64 (+.f64 16316775383/10000000000 (.f64 134362287316698645903/100000000000000000000 (pow.f64 x 2))) (.f64 1427746267379707/1000000000000000 x)))

Compiler

Compiled 2714 to 2114 computations (22.1% saved)

regimes131.0ms (4.6%)

Accuracy

Total 0.0b remaining (7.7%)

Threshold costs 0.0b (7.7%)

Counts

45 → 1

Compiler

Compiled 1805 to 1400 computations (22.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	15	20
2	14	20

end76.0ms (2.6%)

Compiler: Compiled 81 to 62 computations (23.5% saved)

Details

analyze5.0ms (0.2%)

sample1.5s (52.5%)

simplify99.0ms (3.5%)

prune8.0ms (0.3%)

localize19.0ms (0.7%)

series17.0ms (0.6%)

rewrite10.0ms (0.4%)

simplify131.0ms (4.6%)

prune224.0ms (7.8%)

localize48.0ms (1.7%)

prune214.0ms (7.5%)

localize13.0ms (0.5%)

series11.0ms (0.4%)

rewrite29.0ms (1%)

simplify117.0ms (4.1%)

prune201.0ms (7.1%)

regimes131.0ms (4.6%)

simplify2.0ms (0.1%)

end76.0ms (2.6%)

Profiling